def test_rotation_3d():
"""
A sanity test - when V2_REF = 0 and V3_REF = 0,
for V2, V3 close to the origin
ROLL_REF should be approximately PA_V3 .
(Test taken from JWST SIAF report.)
"""
def _roll_angle_from_matrix(matrix, v2, v3):
X = -(matrix[2, 0] * np.cos(v2) + matrix[2, 1] * np.sin(v2)) * \
np.sin(v3) + matrix[2, 2] * np.cos(v3)
Y = (matrix[0, 0] * matrix[1, 2] - matrix[1, 0] * matrix[0, 2]) * np.cos(v2) + \
(matrix[0, 1] * matrix[1, 2] - matrix[1, 1] * matrix[0, 2]) * np.sin(v2)
new_roll = np.rad2deg(np.arctan2(Y, X))
if new_roll < 0:
new_roll += 360
return new_roll
# reference points on sky and in a coordinate frame associated
# with the telescope
ra_ref = 165 # in deg
dec_ref = 54 # in deg
v2_ref = 0
v3_ref = 0
pa_v3 = 37 # in deg
v2 = np.deg2rad(2.7e-6) # in deg.01 # in arcsec
v3 = np.deg2rad(2.7e-6) # in deg .01 # in arcsec
angles = [v2_ref, -v3_ref, pa_v3, dec_ref, -ra_ref]
axes = "zyxyz"
M = rotations._create_matrix(np.deg2rad(angles) * u.deg, axes)
roll_angle = _roll_angle_from_matrix(M, v2, v3)
assert_allclose(roll_angle, pa_v3, atol=1e-3)
def test_euler_angles(axes_order):
"""
Tests against all Euler sequences.
The rotation matrices definitions come from Wikipedia.
"""
phi = np.deg2rad(23.4)
theta = np.deg2rad(12.2)
psi = np.deg2rad(34)
c1 = cos(phi)
c2 = cos(theta)
c3 = cos(psi)
s1 = sin(phi)
s2 = sin(theta)
s3 = sin(psi)
matrices = {
'zxz':
np.array([[(c1 * c3 - c2 * s1 * s3), (-c1 * s3 - c2 * c3 * s1),
(s1 * s2)],
[(c3 * s1 + c1 * c2 * s3), (c1 * c2 * c3 - s1 * s3),
(-c1 * s2)], [(s2 * s3), (c3 * s2), (c2)]]),
'zyz':
np.array([[(c1 * c2 * c3 - s1 * s3), (-c3 * s1 - c1 * c2 * s3),
(c1 * s2)],
[(c1 * s3 + c2 * c3 * s1), (c1 * c3 - c2 * s1 * s3),
(s1 * s2)], [(-c3 * s2), (s2 * s3), (c2)]]),
'yzy':
np.array([[(c1 * c2 * c3 - s1 * s3), (-c1 * s2),
(c3 * s1 + c1 * c2 * s3)], [(c3 * s2), (c2), (s2 * s3)],
[(-c1 * s3 - c2 * c3 * s1), (s1 * s2),
(c1 * c3 - c2 * s1 * s3)]]),
'yxy':
np.array([[(c1 * c3 - c2 * s1 * s3), (s1 * s2),
(c1 * s3 + c2 * c3 * s1)], [(s2 * s3), (c2), (-c3 * s2)],
[(-c3 * s1 - c1 * c2 * s3), (c1 * s2),
(c1 * c2 * c3 - s1 * s3)]]),
'xyx':
np.array([[(c2), (s2 * s3), (c3 * s2)],
[(s1 * s2), (c1 * c3 - c2 * s1 * s3),
(-c1 * s3 - c2 * c3 * s1)],
[(-c1 * s2), (c3 * s1 + c1 * c2 * s3),
(c1 * c2 * c3 - s1 * s3)]]),
'xzx':
np.array([[(c2), (-c3 * s2), (s2 * s3)],
[(c1 * s2), (c1 * c2 * c3 - s1 * s3),
(-c3 * s1 - c1 * c2 * s3)],
[(s1 * s2), (c1 * s3 + c2 * c3 * s1),
(c1 * c3 - c2 * s1 * s3)]])
}
mat = rotations._create_matrix([phi, theta, psi], axes_order)
assert_allclose(mat.T,
matrices[axes_order]) # get_rotation_matrix(axes_order))